Optimal Transport vs Many-to-many assignment for Graph Matching

Anca-Ioana Grapa 1, 2 Laure Blanc-Féraud 1, 2 Ellen van Obberghen-Schilling 3, 2 Xavier Descombes 1, 2
1 MORPHEME - Morphologie et Images
CRISAM - Inria Sophia Antipolis - Méditerranée , IBV - Institut de Biologie Valrose : U1091, Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : Graph matching for shape comparison or network analysis is a challenging issue in machine learning and computer vision. Generally, this problem is formulated as an assignment task, where we seek the optimal matching between the vertices that minimizes the difference between the graphs. We compare a standard approach to perform graph matching, to a slightly-adapted version of regularized optimal transport, initially conceived to obtain the Gromov-Wassersein distance between structured objects (e.g. graphs) with probability masses associated to the nodes. We adapt the latter formulation to undirected and unlabeled graphs of different dimensions, by adding dummy vertices to cast the problem into an assignment framework. The experiments are performed on randomly generated graphs onto which different spatial transformations are applied. The results are compared with respect to the matching cost and execution time, showcasing the different limitations and/or advantages of using these techniques for the comparison of graph networks.
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Submitted on : Thursday, September 5, 2019 - 2:34:11 PM
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Anca-Ioana Grapa, Laure Blanc-Féraud, Ellen van Obberghen-Schilling, Xavier Descombes. Optimal Transport vs Many-to-many assignment for Graph Matching. Colloque Gretsi, Aug 2019, Lille, France. ⟨hal-02279634⟩

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